Characterizing the quantum field theory vacuum using temporal Matrix Product states

Abstract

In this paper we construct the continuous Matrix Product State (MPS) representation of the vacuum of the field theory corresponding to the continuous limit of an Ising model. We do this by exploiting the observation made by Hastings and Mahajan in [Phys. Rev. A \textbf{91}, 032306 (2015)] that the Euclidean time evolution generates a continuous MPS along the time direction. We exploit this fact, together with the emerging Lorentz invariance at the critical point in order to identify the matrix product representation of the quantum field theory (QFT) vacuum with the continuous MPS in the time direction (tMPS). We explicitly construct the tMPS and check these statements by comparing the physical properties of the tMPS with those of the standard ground MPS. We furthermore identify the QFT that the tMPS encodes with the field theory emerging from taking the continuous limit of a weakly perturbed Ising model by a parallel field first analyzed by Zamolodchikov.

The results presented in this paper are a significant expansion of arXiv:1608.06544

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Cited by in corpus (5)

• Lecture Notes of Tensor Network Contractions
• Shadow of complex fixed point: Approximate conformality of Q>4 Potts model
• Continuous matrix product operator approach to finite temperature quantum states
• Efficient Quantum Simulation for Thermodynamics of Infinite-size Many-body Systems in Arbitrary Dimensions
• Self-congruent point in critical matrix product states: An effective field theory for finite-entanglement scaling